Factor 144x^2+24x+1

$144 x^{2} + 24 x + 1$

Step 1

Rewrite $144 x^{2}$ as ${(12 x)}^{2}$ .

${(12 x)}^{2} + 24 x + 1$

Step 2

Rewrite $1$ as $1^{2}$ .

${(12 x)}^{2} + 24 x + 1^{2}$

Step 3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$24 x = 2 \cdot (12 x) \cdot 1$

Step 4

Rewrite the polynomial.

${(12 x)}^{2} + 2 \cdot (12 x) \cdot 1 + 1^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 12 x$ and $b = 1$ .

${(12 x + 1)}^{2}$